Question

perpendicular vectors - pythagorean theorem
david walks 3 m north, then turns and walks 4 m east. find his displacement.

Explanation:

Step1: Identify right - angled triangle

The north - south and east - west directions are perpendicular. The two paths of David's walk form the two legs of a right - angled triangle with lengths $a = 3$ m and $b=4$ m.

Step2: Apply Pythagorean theorem

The displacement $d$ is the hypotenuse of the right - angled triangle. According to the Pythagorean theorem $d=\sqrt{a^{2}+b^{2}}$, where $a = 3$ and $b = 4$. So $d=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}$.

Step3: Calculate the value

$\sqrt{25}=5$ m.

Answer:

5 m